TRIGONOMETRY FUNCTIONS & FORMULA || BASIC FORMULA OF TRIGONOMETRY

              TRIGONOMETRY  FUNCTIONS & FORMULA 

  Introduction:  

‘Trigonometry; is Greek derivation of two words ‘TRIGONON’ a triangle  and ‘METRO’ means  I measure therefore, it literally means  ‘I measure a triangle ’.it is supreme important for all mathematics branch and physical science .

Trigonometry is a branch of mathematics that studies relationship of length and angle of triangle.

Here , the angle is trigonometry are represented by Greek symbol θ(theta), (alpha), (beta), (gamma).

  I.     RELATION BETWEEN SIDES OF TRIANGLE

In a right-angled triangle, the ratio of it’s sides with respect to its angle is constant. If the angle is varied the ratio of the side is also changed , relation of the side is

I.    TRIGONOMETRIC FORMULA: 

1.     Sin θ = P/H

                 

2.       cos θ = B/H

3.       tan θ= P/B

4.    cosec θ= H/P

5.      sec θ=  H/B

6.       cot θ = B/P

II.      TRIGONOMETRIC FORMULA

perpendicular = P  and Hypotenuse = H & Base = B

* sin θ = 1 / cosec θ

* cos θ = 1 / sec θ

* tan θ = 1 / cot θ

* cosec θ = 1 / sin θ

* sec θ = 1 / cos θ

* cot θ = 1 / tan θ

 And

      Sin θ × cosec θ = 1

      Cos θ × sec θ = 1

      tan θ × cot θ =1

some important formula of trigonometry

1.   sin (A + B) =sin A . cos B + cos A . sin B

2.  sin (A - B) = sin A . cos B - cos A . sin B

3.  cos (A + B) = cos A . cos B - sin A . sin B

4.  cos (A- B) cos A . cos B + sin A. sin B

5.  tan (A+ B)=  (tan A + tan B) / (1 - tan A . tan B)

6.  tan (A-B) =  (tan A - tan B) / (1 + tan A . tan B)

7.  tan A ± tan B = sin(A ± B) / cos A . sin B

8.  sin 2A = 2 sin A . cos A

9.  cos 2A= cos²A - sin²A

                = 2 cos²A – 1

                = 1 – 2 sin²A

10.  tan 2A =  (2 tan A) / (1 - tan²A)

11.  sin 3A = 3 sin A - 4 sin³ A

12.  cos 3A =  4 cos³ A - 3 cos A

13.  tan 3A =  (3 tan A - tan³ A) / (1 - 3 tan²)

14.  sin A + sin B = 2 sin[(A+B) / 2 ]. cos [(A-B) / 2]

15.  sin A - sin B = 2 sin[(A-B) / 2 ]. cos [(A+B) / 2]

16.  cos A + cos B = 2 cos[(A+B) / 2 ]. cos [(A-B) / 2]

17.  cos A - cos B = -2 sin[(A+B) / 2 ]. sin [(A-B) / 2]

18.  sin A . sin B = 1/2 [cos (A – B) – cos (A + B)]

19.  cos A . cos B = 1/2 [cos (A + B) + cos (A - B)]

# SOME OTHER SYSTEM

In the system ,

· one right angle  divided into 60 parts which are called ‘degrees’.

· Each part divided into 60 part which are called

are called minutes.

· Each minutes again divided  into 60 part which are called seconds .

Parts so divided respectively are denoted as:

One degree (1°), one minute (1) and one seconds (1")

It means,

•  1 right angle = 90°(90 degrees)
• 1° (1 degree) = 60' (60 minutes)
• 1 minute (1) = 60" (60 seconds)

In trigonometry, mostly this system is used.

And also 1 thing : π= radians

                      Where the values of radians is 22/7 & 3.142

You always memorized some values 0⁰,30⁰,45⁰,60⁰,90⁰

θ	0⁰ or 0	30⁰ or π/6	45⁰ or π/4	60⁰ or π/3	90⁰ or π/2
sin θ	0	½	1/√2	√3/2	1
Cos θ	1	√3/2	1/√2	1/2	0
tan θ	0	1/√3	1	√3	Undefined
cosec θ	undefined	2	√2	2/√3	-1
Sec θ	1	2/√3	√2	2	Undefined
Cot θ	undefined	√3	1	1/√3	0